Declarations

scope. The source is a standalone analytical interface manuscript. Its submission claim must be the theorem package printed here, not a completed gravitational one-loop or ultraviolet construction. Responsible author metadata and independent technical review remain necessary.

scope. Cheung references identify supplied versions, excerpts, or summaries. Their full parent proofs and artifacts are not independently certified. The supplied OpenAI catalogue attribution is not authenticated here and is not a premise. Stable archival sources should accompany actual review.

. Elementary linear-algebra, distributional, and formal-series arguments are not claimed as new foundational theorems. Corresponding supplied arguments are attributed. The contribution is their coherent proof package and application contract.

scope. No field instrument, calibrated apparatus, quantum-return decoder, or physical code-recovery task is constructed. A correlator coefficient is not automatically a probability law; measurement implementation remains separate.

scope. No new metric, gravitational Hamiltonian, de Sitter state, spacetime-emergence theorem, entanglement wedge, island, Page curve, or evaporation model is derived.

. No successful pdflatex build, numerical or symbolic execution, proof-assistant verification, independent referee validation, registration, or journal acceptance is asserted.

. Citing N. Cheung does not attribute authorship of this revision to that author. Authorship authorization must be supplied by the submitting author.